Differential Equation First Order Linear

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Homework Help Overview

The discussion revolves around solving a first-order linear differential equation of the form y*e^(x^2)*dy/dx=x+xy. Participants are exploring methods to manipulate the equation into a recognizable form for solving.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • One participant attempts to modify the equation to fit the standard form of a first-order linear differential equation, expressing concern about the transformation process. Another participant suggests factoring the equation to facilitate separation of variables.

Discussion Status

Participants are actively engaging with the problem, with one providing an alternative approach to factor the equation. There is a sense of exploration regarding different methods, but no consensus has been reached on the best approach yet.

Contextual Notes

Participants are working under the constraints of homework guidelines, which may limit the types of solutions or methods discussed. There is an ongoing examination of assumptions related to the equation's structure and potential methods for solving it.

ruiwp13
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Homework Statement



Solve the following differential equation: y*e^(x^2)*dy/dx=x+xy

Homework Equations



y'+P(x)*y=Q(x)

The Attempt at a Solution



I tried to modify the equation to match the first order linear one, and I got:

e^(x^2)*dy/dx=x/y+x (divided everything by y),

but now I get:

dy/dx-x*1/y=e^(-x^2)*x

so instead of the normal form, I have now y'-P(x)*1/y = Q(x).

Did I do something wrong or missing something?

Thanks in advance
 
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ruiwp13 said:

Homework Statement



Solve the following differential equation: y*e^(x^2)*dy/dx=x+xy

Homework Equations



y'+P(x)*y=Q(x)

The Attempt at a Solution



I tried to modify the equation to match the first order linear one, and I got:

e^(x^2)*dy/dx=x/y+x (divided everything by y),

but now I get:

dy/dx-x*1/y=e^(-x^2)*x

so instead of the normal form, I have now y'-P(x)*1/y = Q(x).

Did I do something wrong or missing something?

Thanks in advance

Why don't you just factor x+xy into x(1+y) and separate?
 
Dick said:
Why don't you just factor x+xy into x(1+y) and separate?

∫y/(1+y) dy=∫e^(-x^2)*x dx

Like this?
 
ruiwp13 said:
∫y/(1+y) dy=∫e^(-x^2)*x dx

Like this?

Yes, like that.
 

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